Tanya's song "Dreams to Dream" in Fievel Goes West. It is virtually completely pointless to the story, but is such a heartwarming scene. It's pretty telling when Cat R. Waul, who has been maintaining a very unflattering view of mice up to this point, hears it and is moved to tears.
The ending of Fievel Goes West. Fievel and Wylie Burp are watching the sunset and Wylie offers his badge to Fievel, but the mouse can't accept it because he's not a hero like Wylie. Wylie replies;
"Maybe not. Maybe a real hero's the last to hear about it. You pulled me out of a gutter, and for that I owe you some thanks. Just remember, Fievel, one man's sunset is another man's dawn. I don't know what lies beyond those hills, but if you ride yonder, head up, eyes steady, heart open, I think one day you'll find that you're the hero you've been lookin' for."
Plus, Fievel flipping his hat back to the blue at the end was sweet, like he learned he could be a hero by being himself.
Especially touching is that this was Jimmy Stewart's final film role, effectively symbolizing the passing of the baton from his generation of actors to the new.